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Title: Slash distributions, generalized convolutions, and extremes Authors:  Marek Arendarczyk - University of Wroclaw (Poland) [presenting]
Tomasz Kozubowski - University of Nevada Reno (United States)
Anna Panorska - University of Nevada (United States)
Abstract: An $\alpha$-slash distribution built upon a random variable $X$ is a heavy-tailed distribution corresponding to $Y=X/U^{1/\alpha}$, where $U$ is a standard uniform random variable, independent of $X$. We point out and explore a connection between $\alpha$-slash distributions, which are gaining popularity in statistical practice, and generalized convolutions, which come up in probability theory in connection with generalizations of the standard concept of convolution of probability measures. Our theoretical results are illustrated by several examples involving standard and novel probability distributions and extremes.